Hierarchical Decomposition and Multidomain Formulation for ...strategic.mit.edu/docs/2_34_JMD_091003_Sustainable_Systems.pdf · hierarchical decomposition that includes multilevel

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Anas Alfarise-mail: [email protected]

Afreen Siddiqie-mail: [email protected]

Charbel Rizke-mail: [email protected]

Olivier de Wecke-mail: [email protected]

MIT Engineering Systems Division,Building E40-261,

77 Massachusetts Avenue,Cambridge, MA 02139

Davor SvetinovicMASDAR Institute of Science and Technology,

P.O. Box 54224,Abu Dhabi, UAE

e-mail: [email protected]

Hierarchical Decomposition andMultidomain Formulation for theDesign of Complex SustainableSystemsDesigning a large-scale complex system, such as a city of the future, with a focus onsustainability requires a systematic approach toward integrated design of all subsystems.Domains such as buildings, transportation, energy, and water are all coupled. Designingeach one in isolation can lead to suboptimality where sustainability is achieved in oneaspect but at the expense of other aspects. Traditional ad hoc allocations of designparameter precedence and dependence cannot be used for cases where new (instead ofonly mature) architectures are to be explored. A methodology is introduced for addressingdesign problems of complex sustainable systems that is comprised of, on the one hand, ahierarchical decomposition that includes multilevel abstraction and design parameteridentification, and on the other hand, a multidomain formulation, which includes param-eter dependency identification, design cycle identification and decision structuring, andscoping. The application of the methodology for the design of a new urban development,Masdar City in Abu Dhabi, with over 220 different form and behavior parameter sets isshown. �DOI: 10.1115/1.4002239�

IntroductionFor creating sustainable complex systems, it is important to

ake an integrated, multidomain design approach. In large-scaleomplex systems, a number of subsystems �often also complexnd large in their own right� interact and function together. Fornstance, in a city, the building, transportation, energy, and waterystems are different complex systems �or domains� that workogether so that the city can function as a whole. If it is desirableor sustainability to reduce emissions, decrease waste, and re-ource consumption, then it becomes imperative to undertake annclusive approach across all the domains of the system. Other-ise, if each domain is designed independently to conform to a setf sustainability standards, it may very well be that sustainabilityequirements in one domain conflict with another and that theverall system is less sustainable than it could be. For example, aery stringent requirement for water recycling and reuse mightntail very high energy and capital equipment requirements thatre in conflict with a low environmental footprint. The overallehavior of the large-scale system is then far from ideal or per-aps in some cases could even be worse �1�.

This problem of “balancing” the design in a complex systemas been the subject of significant attention and research in theast few decades �2�. Much of the work has been focused onystems such as spacecraft, aircraft, and buildings �3,4�. In thisork, however, we address systems that can also be referred to as

ystem of systems �SoS� where each subsystem is a different, fullyunctioning system in its own right �5�. Specifically, we look athe case of designing a future city where its building, transporta-ion, water, and energy systems have to be designed so that theity has minimum emissions and high efficiency in the use andonsumption of resources �such as that of energy, water, and otheraterials�. In such problems, it is critical to balance the design of

ll the systems so that the sustainable design of one does notmpose unnecessary requirements on the other.

Contributed by the Mechanisms and Robotics Committee of ASME for publica-ion in the JOURNAL OF MECHANICAL DESIGN. Manuscript received January 2, 2010;nal manuscript received July 6, 2010; published online September 16, 2010. Assoc.
ditor: Steven J. Skerlos.
ournal of Mechanical Design Copyright © 20

aded 09 May 2011 to 18.111.89.107. Redistribution subject to ASME

When all the systems are treated at a similar level of detail andtheir inter-relationships explicitly understood, it would be possibleto identify the key parameters that collectively provide the great-est influence on the design. The need for eliciting the key drivingvariables across the systems �which will also be called domains inthe context of our work� is fundamental if a systematic approachtoward a truly sustainable design is to be adopted. This work ofparameter identification and modeling of coupling relationshipsprecedes what is typically understood as mathematical modelingand optimization.

In an integrated, multisystem �domain� design approach, thechallenges of scale and scope are prominent. If one is to modeleach system in detail, then the design space quickly becomes pro-hibitively large when multiple systems/domains are included. An-other problem is that of the design parameter hierarchy. It is oftenthe case that an ad hoc approach is used in defining a top levelsystem whose design then dictates the design of the next systemand so on. In some instances, tradition and routine also drive thehierarchy of choice in terms of which system is designed �or itsvariables set� first and so on. This is usually acceptable when thesystem design and architecture are mature and the new design isnot fundamentally different from experience. However, for caseswhere it is permissible and, in fact, desirable to explore com-pletely new architectures, it can often be unclear as to how thehierarchy of the design parameters should be set. This difficulty isonly compounded with the complexity and size of the problembeing addressed, and the relationships that exist between param-eters across different domains.

A simple example of a hypothetical building system can beused to illustrate this discussion. It is assumed that a new buildingis to be designed in which its municipality-supplied fresh waterconsumption is to be significantly reduced. This problem is moti-vated by a case described in Ref. �6�. The water reduction isachieved through re-use of treated gray-water and high efficiencyappliances and fittings. The building can have three types ofspaces �zones�: offices, retail areas, and restaurants. Each type hasits own requirements for water and produces used water �i.e.,gray-water� of different quality. For sustainability, it is also de-
sired that all the energy needs for water treatment within the
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uilding are fulfilled through electric power generated from pho-ovoltaic systems installed on the building’s roof. It is also as-umed that the size of the building, the floor area mix �in terms offfice area, retail area and restaurant area�, the water treatmentptions, and re-use quantities are open for design decisions. Fig-re 1 shows a simple schematic of the system under consideration.

There are three domains: building, water, and energy in thisroblem that are closely inter-related. Setting the design param-ters for one will impose requirements for the others. For instance,f one is to set the building zone mix �in terms of floor area ofach type�, then there will be implications for the required waterupply and therefore treatment units and electricity generation ando on. Similarly, if one were to set the power generation capacityrst, then there will be implications on quantity of treated waterhich in turn will dictate amount of water that can be re-used. In

ummary, if the design space of the problem is relatively openi.e., most of the parameters are not constrained a priori�, then it isot immediately obvious which design decisions should be takenrst. It is, however, clear that an ad hoc approach toward setting

he parameter hierarchy �i.e., deciding the order in which param-ters are given design values� can lead to suboptimal solutions.espite advances in all-in-one approaches to design optimizationhen the number of design parameters exceeds a few dozen, theroblem becomes too large for convergence to be achieved inseful time.

For large-scale systems, where new architectures can be ex-lored, and a number of different domains �each equally importantnd also complex� are intimately related, it is vital to take a sys-ematic approach. Our work describes a systematic frameworkpplied in a consistent manner across all constituent systems of aarger complex system so that the structure and relationships ofhe design parameters can be organized. This organization thenelps toward structuring the flow of design decisions.

Our methodology consists of first decomposing the system byreating an abstraction of the design problem levels through these of object-process methodology �OPM� �7�. The object-processiagrams �OPDs� of the overall problem and then of specific sys-ems to be designed are created in a consistent manner at the sameevel of decomposition. This results in the identification of the

ost relevant objects �form� and process �behavior� parameters athe same level of detail across all systems and allows for mean-ngful construction of dependency relationships. The form andehavior parameters of each system �or domain� are then formu-ated and assembled in a metamatrix, the multidomain matrixMDM�, that consists of the intradomain design structure matricesDSMs� �8� and interdomain domain mapping matrices �DMMs�9�. The completed MDM is then partitioned and clustered usingeachability matrices. The result is a sequencing and grouping ofhe parameters so that an ordering of design cycles �smaller sub-roblems within a larger design problem� becomes apparent. Each

Fig. 1 Sustainable building design with w

esign cycle is then further analyzed to allow for validating and

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structuring design decision hierarchy. A traceable and justified or-der of design decisions and cycles for the multidomain, complexsystem design problem is thus created.

The methods, of OPM, DSMs, and reachability matrices, dis-cussed in this paper are known and separately developed in litera-ture. This work, however, brings them together to show how asystematic and traceable methodology can be constructed forstructuring large-scale design problems. While the proposedmethod is applicable for any relevant design problem, it can beespecially useful in the context of sustainable design. As discussedearlier, an integrated cross-domain approach is needed to createoverall sustainability in engineered systems. Cross-domain inte-gration, however, creates a larger design space that needs to besystematically handled. The methodology proposed offers a struc-tured way for systematically approaching such large-scale designproblems.

In Sec. 2, we describe the details of our method in a stepwisefashion, and then in Sec. 3, we discuss its application to an urbandevelopment project currently ongoing in the UAE. In Sec. 4, wediscuss the strengths and limitations of our approach and providea roadmap for future work.

2 MethodologyOur proposed methodology for systematically addressing a

complex, multidomain design problem essentially consists of thefollowing steps �depicted in Fig. 2�:

1. Hierarchical decomposition of each system �domain�, whichincludes the following

a. multilevel abstractionb. identification of form parameters �FPs� and behavior pa-

rameters �BPs�

2. Multi Domain Formulation which includes the following:

a. identification of information flow �dependency� betweenparameters

b. design cycle identification through sequencing and clus-tering of the parameters

c. decision structuring and scoping of design cycles throughhigher order parameter dependency analysis

2.1 Hierarchical Decomposition. We use the term “decom-position” to refer to the act of breaking a large problem into a setof smaller problems or elements. Considerable literature exists onthe subject of design decomposition. The principal research in thisliterature was initiated with the work of Alexander �10� on usingnetworks for representing and decomposing design problems ac-cording to customer needs. In system theory a well-establisheddecomposition approach is the what-how method. The “what” is a

er reuse and treatment with clean energy

problem-oriented question that conveys a goal that in turn refers

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o the system’s function. On the other hand, the “how” is aolution-oriented question that conveys how the objective is metnd in turn refers to a system’s architecture. Axiomatic design �11�s an example of a system decomposition method that implementshe what-how paradigm where the what is represented by func-ional requirements and the how is represented by designarameters.

In our proposed methodology, we will use a systems modelinganguage to represent our design decomposition levels and param-ters. Several system modeling languages have been developedor general-purpose systems, each with its own semantics andotation, these include unified modeling language �UML�, sys-ems modeling language �SysML�, and the object-process meth-dology �OPM�.

In our methodology, we will focus on OPM because it providess with a framework for formally defining whats and hows andeatures a concise set of symbols that form a language for express-ng the system’s building blocks and how they relate to each otheroth formally and behaviorally.

Building blocks in OPM include objects and processes. Objectsre what a system or product is �physical or informatical�, whilerocesses are things that transform objects. Processes can trans-orm an object in three different ways: by creating it, by destroy-ng it, or by affecting it in some way. In OPM objects and pro-esses together describe a system’s function, form, and behaviorn a single, consistent, domain-neutral model. In OPM graphicalomenclature rectangles refer to objects, while ellipses refer to

ig. 2 Methodology overview: hierarchical decomposition andultilevel formulation

rocesses. OPM uses two types of links to connect entities with

ournal of Mechanical Design


each other: structural links and procedural links. Structural linksrelate objects to other objects and processes to other processes andcan express static relations between pairs of entities. Procedurallinks, on the other hand, are links used to connect entities todescribe the behavior of a system. They link an object to a processand can indicate a change in the state of the object �7�.

2.1.1 Multilevel Abstraction. According to Eggert �12�, thefunction of a system is what it is expected to perform. Functiondescribes the rationale behind a system existence, the intent forwhich it was built, the purpose for which it exists, and the goal itserves �7�. When dealing with functions, we are concerned withwhat the system does and why it does it and not with how it doesit.

The system’s architecture is the general system’s form-behaviorcombination that helps it achieve its function. It represents thething that is eventually implemented and operated in a solutionspecific domain. Form, according to Crawley �13�, refers to thephysical or informational embodiment that exists or has the po-tential to exist. On the other hand, the behavior of a system de-scribes how an object operates to achieve its function. Functionand behavior are not synonymous. While function is derived fromthe system’s goal; behavior is how the system behaves to achievethe system’s function. Performance of a system therefore becomesan attribute of a system’s actual or expected behavior that mea-sures its effectiveness.

In the general context of designing, functions, representedthrough requirements R �where R is a set�, are to be transformedinto a system form F that can produce the required functions. Aset of design requirements R might not have a unique form Fsolution but a multiplicity of solutions. Two different forms canachieve the same function through different behaviors. The behav-ior of the system B can then be compared with and evaluatedagainst the functional requirements R to determine if the synthe-sized form achieved the required functions.

Form-behavior decomposition usually refers to hierarchicallyrelated subsystems presented schematically as a pyramid whosetop is the higher-level system and whose base is the lower levelsubsystem. Subsystems may correspond to form components andcan also correspond to system behaviors. System decompositionrelies highly on system designer’s experience. It is not typical thatdesigners persistently follow a top-down decomposition processto the level of single parameters. They usually iterate between theupper and lower system decomposition levels according to whatthey can potentially learn within the process about the implica-tions of some of their architectural decisions and any legacy ele-ments to be incorporated.

In our methodology we propose an OPM template that providesa framework for decomposing a systems whats and hows withminimal ambiguity and at different levels of granularity. The levelof abstraction will be determined based on �a� the detail needed toassist decisions made by engineers and urban planners and �b� themanageability and number of elements. The template describes adesign state Ds at a particular point in time and maps the systemarchitecture �form-behavior combination� to the system’s require-ments and identifies its relation to the context in which the systemwill operate. Using the proposed OPM template, new form orbehavior parameters can be added, modified, or even omitted asthe design evolves. There are three main sets that capture a designstate, these include the requirements set R, the context set C, andthe designed system set S �Fig. 3�. Both R and C provide input tothe system set S parameters. The nature of these sets and thenumber of entries in each are closely coupled with the purposebeing modeled and the complexity of the system being formu-lated. Using the three design sets, a descriptive measure of thedesign state Ds can be provided at any given instant in time Ds= �R ,C ,S�.

2.1.2 Parameter Identification. Within the proposed template,
the requirements set R is the cornerstone of the systems design
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nd engineering process. Buede �14� assumed four categories ofequirements: input/output, technology and systemwide, trade-off,nd test requirements. The context set C is the set of entities thatnteract with the systems through its external interfaces. The con-ext entities can impact the system as a form of input and bempacted by its outputs. The context set could include operands inhe context environment, external systems, or the system users.he system design set S includes the system’s form set Sf as wells the system’s behaviors set Sb.

Identifying design parameters is the main objective of our de-omposition. We consider two main classes of design parameters:Ps and BPs. FPs describe the systems attributes, components,nd relationships, while BPs describe behavior characteristics thatre derived or expected from the system’s form. FPs are essentialo the synthesis activities later in the modeling phase, while BPsre important for the analysis activities. Each component can havene or more form parameters FP that describe the componentsttributes. The system form executes certain system behaviors.he system’s behavior set includes the anticipated system behav-

ors. Each anticipated behavior can have one or more behaviorarameters BP that measure the behavior characteristics. Each ofhese sets should include elements at the level of granularity avail-ble at that level of the design.

To illustrate the use of this template, consider the design prob-em introduced in Sec.1. The problem can be abstracted into twoevels. For brevity we will focus here on level 1. The context setould include the city urban system, the city water system, and

he energy system. The requirements set would include functionalequirements such as accommodation, water and energy opera-ions, and requirements. The system set would include high levelubsystems, as well as high level system behaviors. The form setould include the building spatial system, water system, and en-

rgy system. The behavior set would include the high level utility,rea consuming, water consuming, energy consuming, and costingnd emitting behaviors �Fig. 4�. In the second level, we have moreetailed parameters, for example, the spatial system, for example,ncludes several FPs, such as the zone mix, that will affect severalPs, such as water demand and building cost.

2.2 Multi Domain Formulation. Formulation can be defineds the act of systematized expression. It can imply an arrangementf a group of elements in a prescribed manner or for a specificurpose �15�. In the process of designing a complex system, it isecessary to structure the information and different parametersxtracted at the decomposition phase, as well as describe and planhe sequence of applications and interactions.

Our proposed method views the design of a large-scale complexystem as an interaction between parameters within a set of design

Fig. 3 OPM deco

ycles. Design cycles and iterations are part of any design process.

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They can be defined as the repetition of activities to improve anevolving design �16�. A design cycle can be modeled by tracingdesign information flow between different design activities andparameters.

2.2.1 Parameter Dependency Identification. Eppinger �17�identified three types of flow dependencies: serial �dependent�,parallel �independent�, and coupled �interdependent�. Three typesof parameter dependencies can also be identified: These are formto form, behavior to behavior and form to behavior. Form to formdependencies identify which FPs provide information to a particu-lar FP. Behavior to behavior dependencies identify which BPsprovide information to a particular BP. Form to behavior depen-dencies identify which FPs provide information to a certain BP.

To understand the design process and the structure of informa-tion flow, different representations can be used. One of such rep-resentations is the DSM. The DSM was first introduced by Stew-ard �8�, and since then has gained widespread use in design andorganization of complex systems. The DSM records relationshipsbetween components, tasks, parameters, or other entities that canbe used to describe a system. In our methodology, DSMs are usedto capture flow of information between design parameters and tothen elicit the inherent hierarchy that exists between them.

For a given set of N parameters, the DSM is assembled bylisting them along the columns and rows of an N�N matrix. Thematrix is populated by putting a 1 in the ith row and jth column ifparameter j provides information to parameter i. If there is noinformational dependency between a pair of parameters, their cor-responding matrix element �or cell� is set to zero. The DSM thuscreated shows information flow �i.e., in the example above, infor-mation flows from parameter j to i�.

In our methodology, both the requirements set R and the con-text set C identified in the decomposition provide input to thesystem set S parameters. Therefore, the focus here will be on Sand the list of FPs and BPs obtained from the results of decom-position of the systems, as described in Sec. 2.1. In a multidomainproblem, the DSM concept is extended to that of a DMM in whichthe relationships between parameters of different domains are alsocaptured. A metamatrix called the MDM can then be assembled,in which the DSMs are ordered diagonally, while the DMMs areplaced in off-diagonal positions.

For instance, consider the simple design problem introduced inSec. 1. Suppose that after the decomposition process, as describedin Sec. 2.1, a set of design parameters are obtained for each do-main. Figure 5 shows a sample MDM for this case. The intrado-main parameter dependencies are described in the DSMs �coloredblocks along the diagonal�, while the interdomain relationships

osition template

have been identified in the off-diagonal blocks in DMMs for each



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omain pair. The parameter prefixes W, E, and B �as can be seenn the figure� indicate their domains of water, energy, and buildings was introduced in Sec. 1. For instance, parameter W1 is theuilding water supply volume per day, E1 is waste-water treat-ent energy consumption, and so on.It is interesting to observe from the MDM that the three do-ains are not isolated �the 1s in the white DMM blocks indicate

resence of interdomain relationships�. If each domain had been

Fig. 4 OPM decomposition for s

Fig. 5 A MDM for the sustainab



independent, its design process can proceed without needingmuch interaction from other domains. However, in the case ofinter-relationships if other systems �domains� are neglected up-front, then there may be a need to perform more iterations �thannecessary� to arrive at a feasible solution �which may not be thebest�, or if one domain is given decision priority over others, thenits solution will dictate the design of the others that may lead tooverall inefficient and suboptimal design.

ainable building design example

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2.2.2 Design Cycle Identification. While a good quality MDMan be very valuable in itself, a logical and strategic resequencingf the parameters in the matrix is an essential next step. Thise-ordering of rows and columns �also referred to as partitioning�llows for identifying the inherent feedback that may exist inerms of information flow between a set of parameters. A feedbackxists when there are 1s in the upper diagonal of the matrix �in-icating that an upstream parameter needs information from aownstream parameter�. A lower triangular matrix implies noeedback �thus computation of a design can proceed in a com-letely sequential manner�. Ideally, once a MDM has been parti-ioned, only the inherent feedback in the information exchangetructure of the system remains, while any other feedback effectshat arise purely due to an arbitrary ordering of the parameters inhe matrix are removed. The result is a structured hierarchy ofesign parameters in which only the inherent coupling and feed-acks remain and the decision flow of the design process starts toecome apparent.

Another important step is clustering of the MDM. Clusteringroduces modules, i.e., it produces an ordering such that elementsr parameters that are coupled or have higher degree of interactionithin them �as compared with the rest� are sorted out in groups.his technique helps in managing complexity and helps in orga-izing process flow �18�.

In our framework, sequencing and clustering identify groups ofarameters that constitute a smaller design problem; i.e., theyorm the design space of a design cycle within the larger complexroblem. The concept of reachability matrices �19� is used to iden-ify important parameters belonging to a design cycle. When bi-ary matrices �such as a binary DSMs� are raised to differentowers �using Boolean multiplication� the reachability or pathshat exist between elements can be found. This idea has been theasis of element visibility in complex systems �20,21� A simpleystem, as shown in Fig. 6, can be used to illustrate the concept.

The DSM of the system shown in Fig. 6 is given as matrix A.he square and cube of this matrix is

A2 = �0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

1 0 0 0 0

1 0 0 0 0�, A3 = �

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0�

The matrix A2 essentially shows �with ones in the first columnnd in the fourth and fifth rows� that there is a path, of length 2,hat exists between element 1 and element 4 �along path 1-3-4�nd 5 �along path 1-2-5�. Matrix A3 being entirely zero essentiallyeans that there is no pathway of length 3 between any two

lements in the system.In a system with N elements, the maximum path length that can

xist is N−1. Thus, for a system with N elements, a visibilityatrix V maybe defined as �21�

V = n=1

N−1

An

The visibility matrix shows the direct and indirect dependenciesf all possible path lengths between any two elements. For the

ig. 6 Dependency relationship between five elements inraphical and DSM format

ystem shown in Fig. 6, the V matrix is

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V = n=1

4

An = �0 0 0 0 0

1 0 0 0 0

1 0 0 0 0

1 0 1 0 0

1 1 0 0 0�

It can be seen that element 1 has accessibility to all other ele-ments �2–5�. In the context of design parameters, the DSM inmatrix A shows that parameter 1 directly influences �provides in-formation to� parameters 2 and 3. However, the DSM does notreadily show the indirect dependence that parameter 1 has on 4and 5. The higher successive powers of A and the V matrix col-lectively provide richer insight into the influence chains and canbe useful in determining critical and related parameters �within adesign cycle�. In this case, for instance, it is clear that parameter 1should be treated �or decided� carefully since its impact cascadesthrough every other parameter.

Using this reachability matrix concept design cycle blocks canbe identified. It is important to observe that loops are found withinblocks �design cycles� rather than between blocks. Once thecycles and their parameters are determined, the original BooleanMDM is rearranged to show the separate design cycle blocks. Thistype of clustering can be used to determine the order in whichdesign cycles can be solved. A cycle is thus identified based onhaving both FPs and BPs with FPs generally preceding BPs. Eachcycle block represents a collection of FPs and BPs that need to bedetermined through mathematical modeling. The values of the pa-rameters are then fed into the subsequent design cycles. Once allthe cycles have been computed, a full solution of the problem isobtained. In essence, this approach produces an ordered series ofsubproblems in which the scope of each problem �i.e., collectionof parameters� gets selected based on the inherent information anddependency structure of the larger design space. It is possible thatin a larger multidomain context, the smaller subproblems mayconsist of parameters from different domains �mixing�. It shouldbe noted that in traditional practice, this approach is typically notadopted and each domain �or system� is designed independentlyand design iterations are carried out to simply produce interdo-main functional feasibility.

Figure 7 shows a sample partitioned and clustered MDM ob-tained from the original matrix given in Fig. 5. The set of 22parameters have been grouped into two design cycles. The firstcycle has ten parameters from all the three domains �note theparameter prefixes�. Also there is a group of form parameters�colored in gray� and a group of behavior parameters �in white�.The second cycle has a similar grouping and can be executed afterthe first cycle has been completed.

Fig. 7 MDM with design cycle grouping—note mixing of pa-rameters from various domains in cycle 1 and 2

2.2.3 Decision Structuring and Scoping. The partitioned and



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equenced MDM provides a first estimate of the design cycles inerms of parameters. In a complex system, however, it is impor-ant to take a deeper look at the parameter relationships so thatach design cycle can be better structured and executed within.

Further insight regarding parameter influence and dependencyan be obtained by computing for each parameter, the number ofarameters it influences, and the number of parameters it dependsn. This is similar to the notions of in-degree and out-degree inraph theory. More specifically, one can define

� j =1

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N

aij

�i =1

Nj=1

N

aij

here � j is an indicator of the fraction of total elements to whichlement j provides input �normalized column sum�, �i is the frac-ion of total elements on which element i depends �normalizedow sum�, and aij is an element of a matrix that can be the DSM,power of the DSM, or the V matrix. The term “fan-out visibility”

nd “fan-in visibility” for � and � has also been used in literature21�.

The DSM, its powers, the V matrix, and values of � and �ollectively serve to provide an information basis for guiding thetructure and scope of decisions in a design cycle. For a simplellustration consider again the DSM of the design problem shownn Fig. 5. Using the water domain DSM �upper left 11�11 por-ion of Fig. 5�, the parameter with the highest � was found to be

4 �which was “volume of treated water per day”�. Next, usinghe V matrix, the highest value of � turned out to be for W1volume of city water supplied per day� instead. So if only firstrder interactions are accounted for, W4 is the most influentialarameter. However, when higher order interactions are also fac-ored in, the influence ranking changes and W1 is found to play anven more important role overall. Both of these parameters belongo the first design cycle, as shown in Fig. 7, and should be treatedith due deliberation keeping in mind the impact they will haven the rest of the parameters.

Application: Masdar CityWe have applied our methodology to the ongoing urban devel-

pment project of Masdar City in the outskirts of Abu Dhabi inhe United Arab Emirates �UAE�. The city master plan has beenesigned by the British architectural firm Foster+Partners and isargeted to be a sustainable, zero-carbon, zero waste communityhat will depend on renewable energy sources �22�. The city of

asdar, with a planned area of 6 km2, will be located 17 kmouth-east of Abu Dhabi. It will house 50,000 people, 1500 busi-esses, and a technical university �Masdar Institute of Science andechnology�. It is also expected that more than 60,000 workersill commute to the city daily �23�. The project, initiated in 2006,

s estimated to cost US $22 billion and is targeted for completionn 8 years �23�. An aerial view of the envisioned Masdar City atompletion is shown in Fig. 8.

3.1 Masdar Hierarchical Decomposition. For decomposingasdar City, the template introduced in Sec. 2.2 was used.

3.1.1 Masdar Multilevel Abstraction. Briefly, the decomposi-ion is composed of three sets; a requirements set R, a context set, and a city system set S, which affects and is affected by the cityontext, in order to meet the city functional requirements. Theame template will be used for all lower level decompositions. Inhe Masdar application, three decomposition levels were requiredo reach the described design state. At each level, we will identifyorm components and behavior processes that are relevant for theesign of Masdar City. The OPM approach discussed earlier will
e used to represent the decomposition.


3.1.2 Masdar Parameter Identification. At the highest level�Fig. 9, L1�, two types of behavior were identified: common be-haviors, seen in all subsystems/domains �with different impacts�,and specific behaviors, which are particular to a certain system. Itis also important to note that behaviors of subsystems will aggre-gate to feed behavior of higher-level systems. In our level 1 de-composition of Masdar City, we focused on the system design setof the supersystem level at the city level. Within the context set,the city will interface with existing systems including the AbuDhabi Energy and Water Authority �ADEWA� power grid,ADEWA water distribution system, ADEWA sewage system, theAbu Dhabi transportation network, which includes the road net-work, and the Light Rail Train �LRT�. The requirements setmainly includes the provision of sheltering/accommodating, trans-porting, providing energy/water, for city residents �22�. Within thesystem’s design set, the form set includes four subsystems; theseare the building system, transportation system, energy system, andwater system. These subsystems have several common behaviorsthat are important to evaluate when designing the city sustainably,which include land use, transportation use, energy use, water use,cost, and emissions, as well as the system specific behaviors. Sev-eral dependencies exist between the different subsystems and sub-behaviors which have to be considered at lower leveldecompositions.

In the level 2 decomposition �Fig. 9, L2�, we provided moredetailed views of each of the four subsystems discussed in level 1.A separate OPD was designated for each of them. For brevity, thelevel 2 decomposition discussion will be restricted to the buildingsubsystems. Similar to level 1, level 2 contains three sets. Con-sidering the building system first, the context set will include as-pects such as natural conditions, regulations and codes, and geo-graphic location of the city. All these external factors willinfluence FPs and expected BPs.

The requirements set will consist of aspects such as zone de-pendencies and building area requirements. The city will includedifferent zone types such as the university located within a specialeconomic zone, an associated commercial zone, light industryzones, and residential accommodations. The requirements also ne-cessitate a design with a high quality of urban spaces and build-ings within which a sense of place is created and through which acommunity will prosper and a pleasant environment will beformed making the city a place where people want to live in �22�.The building system OPD consists of two main components and14 behaviors. The two components we identified are type andnetwork. As for behaviors, they are similar to the ones included in

Fig. 8 Grid-based layout of Masdar City at completion, ap-proximately 2016. The enclosed area is approximately 6 km2

and houses 50,000 people. Design of the city to meet high levelsustainability targets is an ongoing design challenge.

level 1 but are split into two behaviors that capture the impact of

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ype and network components.At level 3, we decomposed the type and network components

dentified at level 2 �Fig. 9, L3�. The context and requirements sett this level align with ones at higher levels but are more specific

Fig. 9 Hierarchical decomposition of thedomain level, and L3: component level

nd relate to the subsystems themselves. Level 3 decomposition of

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the type form set within the building system consists of severalzones, such as residential, special economic zones/headquartersSEZ/HQ, parking, and green areas �22�. Each zone consists ofmany cells that require several specifications for land, water,

sdar Building System: L1: city level, L2:
Ma
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ubsystems. The type behavior set includes several behaviors suchs costing, energy consuming, energy generating, emitting, occu-ying, land consuming, transportation capacity consuming, andonstructing. Each of these behaviors exhibits one or more BPs.or example “costing” exhibits maintenance cost per building

ype, operational cost per building type, and capital cost per build-ng type. In turn, costing requires information from FPs such aspecifications, height, and zone type.

The generated OPDs summarize the information identifyinghich FPs are required, as well as which BPs are exhibited. A

imilar level of detailed decomposition was performed for allther three systems. Table 1 represents the number of FPs and BPsor each subsystem.

3.2 Masdar Multidomain Formulation. Here we are con-erned with the design processes formulation and design cycledentification for the design of Masdar City. To achieve this, weill use the DSM methodology discussed in Sec. 2.2.

3.2.1 Masdar Parameter Dependency Identification. Afterdentifying the FPs and BPs in the decomposition stage, we willhen identify the dependencies between the parameters. Unlike theop-down approach taken in decomposition, we will use a bottomp approach in our formulation. We will start first by populatinghe individual system DSMs after which we will populate thenterdomain DMMs to construct the full MDM. The MDM is

Table 1 FPs and BPs for Masdar subsystems „total: 228…

OPD Level 3

ystem Type No. of FPs No. of BPs

uilding Mode 11 14Network 12 8

ater Mode 19 10Network 17 13

nergy Mode 21 10Network 14 13

ransportation Mode 18 16Network 21 11

Fig. 10 Building and transpor



populated with the information identified in the decomposition,which is based on modeling needs and expert judgment of engi-neers and architects who have particular domain knowledge andexperience.

Given the Masdar decomposition discussed in Sec. 3.1, theMDM will be populated with the FPs and BPs identified withinthe OPDs. For brevity, we will focus our discussion on the formu-lation of the building and transportation systems �Fig. 10�. Thesetwo domains were selected because they are highly dependent oneach other based on the correlation between city layout and trans-portation needs. In the MDM of Fig. 10, the building domain FPs�colored in dark gray� are followed by the building domain BPs�colored in white� inside the DSM�B�. Similarly the transportationFPs �colored in light gray� are followed by the transportation BPs�colored in white� in the DSM�T�. Figure 11 summarizes the 16different DSMs and DMMs within the MDM prepared for bothsystems. We can observe from the MDM that the two domains arenot isolated. The intersystem DMMs �gray blocks� have severaldependencies although lower in magnitude than the intrasystemDSM dependencies of each system �white blocks�. Typical intra-system densities are on the order 0.1–0.3 while intersystem depen-dency ratios are on the order 0–0.1.

3.2.2 Masdar Design Cycle Identification. After formulatingthe dependencies within the MDM, we can partition and clusterthe completed MDM to identify inherent feedbacks. For our par-titioning and clustering, we used the algorithm developed by Cho�24�. The algorithm is based on the partitioning method developedby Warfield �19�. The method uses Boolean matrix manipulationand structures the parameters into hierarchical levels. Similar toWarfield, the algorithm uses a reachability matrix to identify pa-rameters belonging to a certain hierarchical level.

Figure 12 shows the unsequenced DSM�B� of the building sys-tem �which will also be referred to as matrix B� on the left. Interms of parameter influence or importance, from simple inspec-tion of the matrix, it can be seen that there are two parameterswhose columns are mostly full. These are parameter BS-1 andBS-12 �which are “cell type assignment” and “zone type assign-ment”�. The almost full columns indicate that these parametersdirectly serve to provide inputs to most other parameters. Theassociated V matrix �also denoted as VB and shown on the right inFig. 12� reveals some additional information. The key informationis that there are indeed four parameters that play an influential role

tation MDM for Masdar City

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ather than just the two that could be identified from the DSM�B�lone. The additional influential parameters that come to light as aesult of computing V are parameters BS-10 and BS-11 �which arelogical dependency” and “architectural dependency”�. Thiseans that in terms of direct impact, the most important variables

n the building system domain are the cell and zone definitionsfor a grid or cell based description of the city’s area�. The choicesade for these two parameters alone will trickle down to affect

lmost every other parameter of the building domain directly. Ad-itionally, the decisions for logical and architectural dependency

ig. 11 DSMs and DMMs within the building and transporta-ion MDM. The Ratio indicates the density of dependenciesithin each submatrix.

Fig. 12 DSM of building system a

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will also play a key role on impacting other variables.The result of the partitioning and clustering is a structured hi-

erarchy of design parameters in which only the inherent couplingand feedbacks remain. The decision flow of the design processstarts to become apparent. Each generated cluster identifies a pos-sible design cycle with a manageable number of parameters. Fig-ure 13 illustrates the output of our MDM clustering in which threedesign cycles �shaded blocks� were identified. The partitioned andclustered MDM shows significant mixing of parameters from thetwo domains, confirming the need for concurrent design. Eachdesign cycle includes a mix of FPs and BPs from both the build-ing and transportation domains. Interestingly, neither the buildingor transportation domains were dominant in any of the cycles.However, the percentage of FPs in the first cluster was higher thanthe last cluster and the opposite was true for the BPs. This isbecause the analysis of behaviors requires the synthesis of formcomponents to be completed first.

As stated earlier, the values of parameters defined within a spe-cific design cycle will feed into following cycles. Therefore, carehas to be taken when identifying design cycles due to the effect itmay have on following design cycles.

3.2.3 Masdar Decision Structuring and Scoping. In order toget further insights about the parameter dependency relationshipsidentified and the design cycles obtained, additional metrics arecomputed. A few illustrative results are discussed here.

Figure 14 shows plots of the ratio � /� �for each of the 43design parameters of the building system�. The ratio of � and �serves to highlight the parameters in terms of their influence ver-sus dependence. Elements with high values of the ratio are thusthose that provide influence to more elements that they depend onand should be given careful attention. The ratios were computedfrom three different matrices. The first line, with black star mark-ers, shows � /� computed from the �DSM� matrix B. In the seconddot marker line, � and � are computed from B2. This is done sothat the relationships that exist at two path lengths between ele-ments get identified. Path lengths greater than 2 are not consideredhere for simplicity. Furthermore, it can be argued that the effect ofthe “influence” or visibility will be diluted with increasing pathlengths. The third line with triangle markers in Fig. 14 is for � /�computed using the full visibility matrix VB for the buildingsystem.

nd V matrix of building system



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It is interesting to note that there are some parameters in whichhe ratio across B, B2, and VB simply decreases �e.g., parametersS-36 to BS-45�. But there are some, e.g., parameters BS-1, BS-8

which is “energy use by buildings”�, and BS-12 in which theecond-order relationship �B2� has a � /� ratio much higher asompared with that obtained from B. This means that there areany more parameters that depend on BS-8 and BS-12 at path

ength 2 than there are parameters that have direct �unit pathength� dependency. We argue that these higher order dependen-ies are particularly important in complex system design forustainability.

In order to get a different sense of the impact of each parameter,he � values for each parameter were computed using the B ma-

Fig. 13 Masdar City—building and trans

2
ig. 14 � /� ratio for building system from matrix B, B , and V


trix and the VB matrix and were then sorted by rank. Table 2shows the top five parameters with highest values of � and also� /� ratios obtained from B and VB.

It is interesting to note that all of the parameters that havehighest �BS-I�VB� ranking are in the first design cycle �as shown inFig. 13�. Furthermore, it can be seen that BS-1 and BS-12 are farmore important than perhaps some others since they have bothhigh direct impact �as can be seen in �BS-I�B�� and high indirectimpact �as can be seen in �BS-I�VB�. Furthermore, for BS-1 the� /� ratio is also among the highest �ranked 5� within the 43parameters. It has a value of 10 when computed for B and a valueof 12.44 when computed for VB �as can be seen in Fig. 14�. Thiscollective information of � and � /� for both B and VB means thatBS-1 has high first order and higher order impact and that it haslow dependency on others. This parameter should thus have a highprecedence in the design decisions. An examination of � /� valuesfor the top ranked BS-33, BS-5, BS-10, and BS 11 shows thatthese parameters have infinite values since these do not have anydependencies �and thus have zero values for ��. Of these param-eters, BS-33 is a behavior parameter, while BS-5, BS-10, andBS-11 are the form parameters. These parameters are thus essen-tially independent control knobs, and in terms of their impact itcan be seen that BS-10 and BS-11 are important �as shown in Fig.12 and also in second column of Table 2�. This information pro-

rtation MDM with design cycle grouping

Table 2 Parameter ranking for highest � and � /� values

No. �BS-i�B� �BS-i�VB� � /�BS-i�B� � /�BS-i�VB�

1 BS-1 BS-10 BS-33 BS-332 BS-12 BS-11 BS-5 BS-53 BS-22 BS-1 BS-10 BS-104 BS-23 BS-12 BS-11 BS-115 BS-34 BS-2 BS-1 BS-1

po

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ides guidance in setting parameter precedence rules within de-ign cycle 1 and can also be a basis for making decisions abouteducing the feedback �through a process called “tearing” �25��.

Figure 15 shows the ratio of � and � for each parameter for theuilding and transportation DMMs. The ratios are computed usinghe DMMs, their squares, and their associated visibility matrices.he interesting thing to note is that � /� for almost every param-ter is higher for the squared and VB matrix case �the second andhird lines are higher on the y-axis than the black lines with aster-sk�. This means that the second and higher order effects appear toominate the influence or impact of the parameters across theomains. In particular, parameters BS-2, BS-6, and BS-9 �all in-luded in design cycle 1� show significant higher order effects.hese parameters are “building height,” “land used by buildingystem,” and “transportation use by building system.” This meanshat when considering the values �through either decisions oromputation� of these parameters, their cross-domain impact onhe transportation system should be factored in.

ConclusionsThe methodology presented in this paper is directed toward

reating sustainable design solutions through an integrated multi-omain approach. Typically, in many integrated design effortshere a large number of design parameters are to be determined,any key parameters are “set” in an ad hoc manner, thus locking

n implications for the subsequent design possibilities. For caseshere entirely new solutions are to be conceived, this kind of

pproach can lead to suboptimal, biased results.In our methodology, the problem of scale and scope, inherent in

arge-scale complex system modeling and design, is managedhrough systemic hierarchical decomposition and a multidomainormulation. The result provides a parameter hierarchy that is re-ective of the influence and dependency of the parameters in theroblem, and the design cycle structuring allows for organizinghe computation and analysis. Using visibility matrices and related

etrics, the decisions regarding individual design parametersithin the cycles can be better informed. Furthermore, the higherrder interactions as they propagate in the DMMs can be veryaluable in understanding the design impacts across domains. Ithould be noted that our proposed methodology is applicable forarly stage assessment when detailed models are not available andnly a framework in terms of directed relationships betweenlements/parameters can be constructed �as is the case forDMs�. The method is particularly helpful when design decisions

etween different domains such as building structures, water, en-

Fig. 15 � /� ratios for building-transportation DMM

rgy, and transportation have to be coordinated within and across.

91003-12 / Vol. 132, SEPTEMBER 2010


The current limitations of our approach include a few aspects.First, performing the decomposition process well is not trivial forcomplex systems, especially when domain neutrality and goodquality abstractions are also desired. Second, creating a high qual-ity MDM is an involved process that requires expert knowledgeand judgment. Third, the design cycle ordering is based on infor-mation exchange alone. It is important to keep in view that abinary DSM based structuring does not differentiate between theintensity and degree of dependence or sensitivity between param-eters. Lastly, in using the V matrix for determining higher orderelement interaction, the magnitude of influence does not get fac-tored in. This type of understanding and insight can only begained through detailed modeling and simulation in which sensi-tivity analysis and other systematic means can be employed fordetermining the impact of change of one parameter on another.The method proposed here is a precursor before a formal designoptimization formulation can be set up.

In our future work, we will improve the design cycle determi-nation process through the use of more sophisticated DSMs �thatwill not be binary�. We will also develop more formal algorithmsbased on visibility concepts but tailored to meet the needs ofcreating better grouping of parameters for design cycles. In thiswork, we have focused on discussing how the interactions alonebetween parameters can be the basis for structuring precedence ofdesign decisions. In future work, the rules for setting parameterprecedence and inclusion in design cycles can also be based onhow a parameter maybe tied to sustainability metrics or goals.Furthermore, this framework as it is applied across all four do-mains �of building, transportation, water, and energy� will be usedto produce a detailed modeling and design tool for Masdar City.This will help in rationalizing and refining current designs andplans for this large-scale undertaking that can serve as a templatefor future sustainable developments.

AcknowledgmentThis work was supported by funding from a MIT-Masdar Insti-

tute of Science and Technology Collaborative Research Grant.

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